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22. Reflectivity measured by imaging radars

Radar equation An imaging radar produces an image in which the digital number at each pixel position is determined by the strength of the radar signal reflected from the corresponding location in the scene.
Digital image files usually are created using the square root of power, since less dynamic range is required for data in this form. For technical purposes, radar performance may be analysed in terms of the power of the reflected signals.
The power received from each radar pulse transmitted may be expressed in terms of the physical parameters of the radar and illumination geometry through the Radar equation.
The received power is a function of radar wavelength and wave polarization, among other variables. Images are built by integrating over many pulses, and the mean power in the image from a terrain patch may be derived from the single pulse radar equation.
For users, the important relationship is the SAR image Radar equation, which has the form:


This expression includes the most important parameter dependencies of concern to a user, which are incidence angle and range. The signal level is very sensitive to the antenna gain pattern, which often is the limiting factor in system brightness calibration.

σ 0 is the radar cross section per surface unit of the target, it is commonly called the radar backscattering coefficient and is a parameter characterising the target.
σ 0 is dimensionless but, as associated to a very high dynamic range (of the order of 105), it is generally expressed in decibels: